GCF and GCF Factoring

GCF Factoring

Finding the GCF

• Find the largest number that divides evenly into all of the terms coefficients

• If all of the terms share the same variable(s) use those with the smallest exponent

Multiple Choice

Find the GCF of 64 and 144

• 8
• 6
• 16
• 2

Multiple Choice

What is the GCF of 18k and 15k³

• 3k²
• 3k³
• 3k
• 5k

Multiple Choice

What is the GCF of

$$24xy^2,\ 36x^3y^5z,\ and\ 18x^2y^3z^2$$  

• $$6xy^2$$  
  

• $$6x^3y^5z^2$$  
  

• $$12xyz$$  
  

• $$12xy^2$$  
  

Factoring a polynomial means expressing it as a product of other polynomials.

• Find the greatest common factor     (GCF).

• Divide the polynomial by the GCF. The quotient is the other factor.

• Express the polynomial as the product of the quotient and the GCF.

Multiple Choice

Factor:
56a³-8a

• 8a²(56a³-8a)
• 8a(7a²-1)
• 8a(7a³-a)
• 8a²(35a²-a)

Multiple Choice

Factor:
 2n²-8n³

• 2n²(n-4n²)
• 2n²(1-4n)
• 2n³(10-8n²)
• 3n(1-4n)

Multiple Choice

Factor 4x - 20

• 4(x -5)
• 4(x + 5)
• 4x(1 - 5)
• 4x(1 + 5)

Multiple Choice

Factor:
p² - 14p

• p(1 - 14)
• 2p(p - 7)
• p²(1-14)
• p(p - 14)

Multiple Choice

Factor Completely:
2x² - 2x - 6

• 2(x + 3)(x - 1)
• 2(x + 2)(x - 3)
• 2(x² - x - 3)
• 2(x² - 2x - 6)

Multiple Choice

Factor by GCF:
17xy - x

• 17(xy - x)
• y(17x - x)
• x(17y - 1)
• not factorable

Multiple Choice

Factor:
2n³+16n+12

• 2n(n³+24n+6)
• 2(n³+8n+6)
• 2n(n³+8n+6)
• 3(n³+8n+6)

Multiple Choice

3x³ + 9x² - 15x 

• x(3x² + 9x - 15) 
• 3x(x² + 3x - 5)
• 3x(x² - 9x + 15) 
• x(3x² -9x + 15) 

Multiple Choice

Factor by using GCF:
10x² + 15x-5

• 25(10x³+45x-15)
• 5(2x³ + 3x²-x)
• x(10x³+15x-5)
• 5(2x²+3x-1)

Multiple Choice

Factor by GCF:
6m² + 16m

• 2(3m² + 8m)
• 2m(3m + 8)
• 2m(3m - 8m)
• not factorable

Multiple Choice

Factor by using GCF:
8n³ + 2n²

• 2n²(4n-1)
• 2n²(4n + 1)
• n²(8n+2)
• 3n(4n+1)